Since you've only got a day I'd do a hike from Yosemite Valley, just because that way you get to see what all the gobsmacking photos are about. Before you arrive though, make sure you check out whether the weekend is a holiday one before you visit though. Yosemite is busy at the best of times, but if it's a holiday weekend you can get hours long traffic tailbacks through the valley, so you have to get there really early. Also if it's hot you'll have to carry a lot of water which might limit your trails. Having said that you can't really go wrong with any trail you choose. Glacier Point/ Sentinel Dome, Yosemite Point, Eagle Peak (this is a big day) are all awesome options. One thing to note is I've always found with hikes in the U.S. have very conservative trail timings if you are fit. By way of example Upper Yosemite Falls has a recommended hike time of 6-10 hours, and I managed it in four pretty comfortably.

1. Clouds Rest - It's about 32km, 1800m gain/loss for a round trip from the Valley floor. It's arguably a better walk and better summit than Half Dome, it just doesn't have those cables or the name recognition.

2. Four Mile Trail to Panorama trail to Mist Trail - 22km, 1000m gain/loss from Valley. The Four Mile Trail (~8km) leads to Glacier Point (where you could buy food if you wanted). Just a round trip on the Four Mile Trail is worth doing. Otherwise continue down the Panorama trail to the Mist Trail. Super great views of Half Dome and three major waterfalls.

3. (Upper) Yosemite Fall trail to Snow Creek trail - ? I don't remember the distance, but it's pretty long, something like Clouds Rest. Really good though, great views. A couple of small side trips are possible, one to the summit of North Dome and another to visit a rare (for granite) natural arch. A shorter alternative is to turn around at Yosemite Point, which is just a little ways up above the top of Yosemite Falls. That's on par with doing the Four Mile Trail as a return walk. Similarly, you could just go up Snow Creek and back.

4. El Capitan - You go up the Yosemite Fall trail and then take a left. You can come back the same way or continue around and return on the decaying Old Big Oak Flat Road. Kind of an adventure. Probably not what you'll do.

Water is generally not an issue, especially in late May. Just take some pills to treat or a small filter if you're concerned. The last reliable water below Clouds Rest is at the trail junction where you leave the John Muir Trail so you'd want to fill up there. And El Cap is dry so if you go that way you'd need to fill up at the top of the Falls. But the rest of hike (1) and pretty much all of hikes (2) and (3) have plenty of water.

You can also skip the overcrowded semi-urban scene in Yosemite Valley and do a walk out of Tuolumne. There are many to choose from. There will be some snow to contend with in late May but it probably won't be too bad this year. Clouds Rest is a much easier walk from that side, both shorter and a lot less elevation.